A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Krylov methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Stable multiscale bases and local error estimation for elliptic problems
Applied Numerical Mathematics - Special issue on multilevel methods
Adaptive Wavelet Methods for Hyperbolic PDEs
Journal of Scientific Computing
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Wavelet-Based Progressive Compression Scheme for Triangle Meshes: Wavemesh
IEEE Transactions on Visualization and Computer Graphics
An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers
SIAM Journal on Scientific Computing
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Numerical solution of the reaction-advection-diffusion equation on the sphere
Journal of Computational Physics
Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Algorithm 929: A suite on wavelet differentiation algorithms
ACM Transactions on Mathematical Software (TOMS)
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A dynamic adaptive numerical method for solving partial differential equations on the sphere is developed. The method is based on second generation spherical wavelets on almost uniform nested spherical triangular grids, and is an extension of the adaptive wavelet collocation method to curved manifolds. Wavelet decomposition is used for grid adaption and interpolation. An O(N) hierarchical finite difference scheme based on the wavelet multilevel decomposition is used to approximate Laplace-Beltrami, Jacobian and flux-divergence operators. The accuracy and efficiency of the method is demonstrated using linear and nonlinear examples relevant to geophysical flows. Although the present paper considers only the sphere, the strength of this new method is that it can be extended easily to other curved manifolds by considering appropriate coarse approximations to the desired manifold (here we used the icosahedral approximation to the sphere at the coarsest level).